The phrase used by the BBC's Ireland correspondent yesterday morning said more than he intended. This was one small step for the Queen, observed Mark Simpson, as Elizabeth II stepped on to Irish soil, but one huge moment in British-Irish history. The echo of Neil Armstrong's famous comment prompts a striking thought. The Sea of Tranquillity is about a thousand times further than the centre of Dublin is from Buckingham Palace. Yet for much of the Queen's long reign, the thought of a royal visit to Ireland was almost as improbable as the thought of a royal visit to the moon.

Yesterday, though, the previously unthinkable happened at last. Good. Inevitably, the first hours spent by a British monarch in Ireland since George V a century ago generated a potent array of British-Irish symbolism. Some of it was discordant. Most of it was not. The Queen wore green – though jade, not emerald. Her plane arrived at Casement aerodrome, named after a man executed for treason against her grandfather. Soldiers of the Irish Republic saluted as she drove up to what was once the Viceregal Lodge for lunch with President McAleese. Then, particularly freighted with meaning, the Queen drove along Irish history's most iconic thoroughfare, O'Connell Street, to the garden of remembrance where, after the playing of the British national anthem, she bowed her head in memory of those who took up arms against her ancestors in 1916 – and before and since.

All this is long overdue. The Irish and British peoples have no transcending quarrel with one another. Nor, nowadays, do the two states. On both sides, there is a craving for normality. A minority, of course, continue to fight old battles. Central Dublin was locked down for the Queen's visit yesterday because of security fears about those who might protest, as a few did. But the barriers to normality are not on the Irish republican side alone. Perhaps the Queen, driving up O'Connell Street, paused to reflect that Catholic emancipation remains unfinished business as long as the Act of Settlement remains unamended. It is high time, if so.

Ireland is changed utterly since the Easter Rising. So is Britain. Yet the history still resonates, and rightly. Some still take all these symbols too seriously, and cannot think outside them. Others do not take them seriously enough, and fail to understand them. Yet while formal events and wreath-layings are the stuff of all state visits everywhere between former adversaries, and although no one is naive enough to think that all passions between Ireland and Britain are now wholly spent, this visit is a powerful and proper attempt at achieving a sort of wider closure between the two states that the two peoples mostly made long ago.